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A long and intense gamma-ray burst (GRB) was detected by INTEGRAL on July 11 2012 with a duration of ~115s and fluence of 2.8x10^-4 erg cm^-2 in the 20 keV-8 MeV energy range. GRB 120711A was at z~1.405 and produced soft gamma-ray emission (>20 keV) for at least ~10 ks after the trigger. The GRB was observed by several ground-based telescopes that detected a powerful optical flash peaking at an R-band brightness of ~11.5 mag at ~126 s after the trigger. We present a comprehensive temporal and spectral analysis of the long-lasting soft gamma-ray emission detected in the 20-200 keV band with INTEGRAL, the Fermi/LAT post-GRB detection above 100 MeV, the soft X-ray afterglow from XMM-Newton, Chandra, and Swift and the optical/NIR detections from Watcher, Skynet, GROND, and REM. We modelled the long-lasting soft gamma-ray emission using the standard afterglow scenario, which indicates a forward shock origin. The combination of data extending from the NIR to GeV energies suggest that the emission is produced by a broken power-law spectrum consistent with synchrotron radiation. The afterglow is well modelled using a stratified wind-like environment with a density profile k~1.2, suggesting a massive star progenitor (i.e. Wolf-Rayet). The analysis of the reverse and forward shock emission reveals an initial Lorentz factor of ~120-340, a jet half-opening angle of ~2deg-5deg, and a baryon load of ~10^-5-10^-6 Msun consistent with the expectations of the fireball model when the emission is highly relativistic. Long-lasting soft gamma-ray emission from other INTEGRAL GRBs with high peak fluxes, such as GRB 041219A, was not detected, suggesting that a combination of high Lorentz factor, emission above 100 MeV, and possibly a powerful reverse shock are required. Similar long-lasting soft gamma-ray emission has recently been observed from the nearby and extremely bright Fermi/LAT burst GRB 130427A.
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